One tabloid, commenting on the plot of a well-known television soap opera, writes about the ins and outs of life on the fictitious square where the characters are supposed to live.

The television critic of another tabloid reviews a show that he thinks fails in its ambitious aims.

Why in the first sentence in the phrase "on the plot" the definitive article is used? It seems to go against the grammar rules known to me. Indeed the plot has not been mentioned before and is not known to a reader, so the indefinite article should be used in such cases, shouldn't it? Interestingly later in the sentence in "of a well-known television soap opera" the usage of the indefinite article is fully in line with the rules as the opera (as well as its plot) is not known to a reader at this time.

Why in the second sentence the author uses again "the" in "The television critic" despite the fact that the television critic has not been mentioned before? The indefinite article would be more appropriate, wouldn't it? And again in "reviews a show" the indefinite article is used in line with the rules as the show (as well as the critic reviewing it) is new to a reader.

5 Answers
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In each of your cases, the basic form is "the X of a Y." That form is indeed correct and implies that there is only one possible instantiation of X given Y.

In one sense of the word "plot," a novel can have only one. A certain specific sequence of events are narrated in "Anna Karenina," not one sequence if you read it in June and a different sequence if you read it in September. So your soap opera example is using "plot" in that sense, and therefore the plot is the one uniquely identified once the soap opera is identified.

Your other example is a bit more subtle. A newspaper may conceivably have more than one reporter covering television. (Variety almost certainly does.) Thus, this sentence is formally correct only if the unspecified newspaper has only one reporter covering television. Thus, unless the writer is confident of that fact, it would be less misleading to use the indefinite article. In practice, however, few newspapers in the US have more than one reporter covering television so that the cultural context suggests that "the" is correct.

Thanks for the explanation. One follow-up question just to check my understanding. Assume that I am describing a trip and so far haven't mentioned neither hills nor houses. If I have got it right, I can say "I turned around and saw a house on a hill" as well as "I turned around and I saw the house on a hill", correct? Even though there are hills with one house and with multiple houses, both alternatives are correct just in the second case I am implicitly communicating that there were only one house on the hill.
– Sergey ZykovAug 9 '18 at 20:07

No. I think you do not quite have it. In the case of a plot, there is one sense of the word "plot" that logically entails that a novel or play or short story necessarily has only one. So "the plot of a novel" is correct English grammar even though one may logically say that no plot has been specifically identified until the novel itself has been identified. Natural languages, however, do not strictly follow the rules of logic: English cannot be construed as the predicate calculus. English says that a novel has only one plot (in one sense of that word) so there is no indeteriminacy. MORE LATER
– Jeff MorrowAug 10 '18 at 2:51

As I tried to make clear, it is a well known fact in the US that it is extremely unlikely that a newspaper has more than one reporter covering television. So unless one is talking about a trade paper like Variety, the assumption in the US would be that one newspaper entails one reporter on the television beat. So it may be treated like the plot-novel situation. It differs, however, in that the rationale is not inherent in the meaning of the words themselves. It depends on cultural context. Consequently, either the definite or indefinite article could be used grammatically. MORE LATER
– Jeff MorrowAug 10 '18 at 3:02

Your example of house and hill strays too far from the logical relation of one novel-one plot. There is nothing in the meaning of "hill" that associates a hill with a single house. Nor in the US is there any cultural expectation that only one house will be built on a hill. In fact, I live in a hilly city, and dozens of houses may be built on a single hill. (Polish Hill probably has hundreds.) So you cannot use what is a rather illogical grammatical peculiarity to imply an unexpected relationship.
– Jeff MorrowAug 10 '18 at 3:13

OK, I see, in structures "the X of a Y" I can use "the" before X even when X has not been mentioned before if there is only one possible instance of X given Y. But, as I believe you tried to make clear with your comments above, the knowledge that there is only one instance of X given Y should be universal (at least within a cultural context). If it is just me who knows that on the hill in question there is only one house or that the newspaper in question has only one reporter covering television, MORE LATER
– Sergey ZykovAug 10 '18 at 12:29

The rule that something must be mentioned before in order to use the refers to just one of the reasons the would be used. the can also be used when the reference is to something that occurs universally (all soap-operas are plot-driven).

Thus, you could also say:

I had to retrieve the password to my account because I'd forgotten it.

even if you had not mentioned a password earlier. All accounts are password-protected.

In the second example, it is typical (if not universally true) for there to be only one TV critic per tabloid. If one of something is typically present in a given context, then the can also be used then too.

Waiter, there's a fly in my soup. I wish to speak to the chef.
--Sir, may I help you?
Chef, there's a fly in my soup.
--Sir, that's a feature, not a bug. We serve only the finest flies to patrons of discerning taste.

As you can see from that last sentence, you can also use the when referring to a specific class of entity (the finest flies), even though you have not mentioned that class previously. You are being specific.

Does this soap opera have one definitive plot? The way your first model sentence is written implies that it does.

Once established, a continuing reference is usually definitive. The continuing reference then uses the definite article. You've mentioned that the indefinite article is appropriate when the reference is not known to the reader at that time. This explains why the phrase "a continuing reference" occurs in the first sentence of this paragraph, but the second sentence has "the continuing reference".

There are, however, other ways that the reader can know at that time that the reference is definitive. Both of your models are examples of another way.

If the well-known soap opera in question has one definitive plot, then "plot of a well-known soap opera" gives the reader enough information at that time to make the definitive article appropriate.

The articles in the model are informative. It's "a" well-known soap opera, so there must be more than one well-known soap opera. The modifier "well-known" isn't enough to establish a definite reference. In contrast, it's "the" plot of that soap opera, so there must be only one definitive plot of that soap opera. It could be the show's only plot, or it could be the only major plot, ignoring sub-plots and side-plots. Identifying the show is enough to identify which plot matters.

When it's just "a" plot of a show, the reader knows that the show has more than one main plot. In that case, the plot isn't made definitive simply by identifying the show.

The television critic of another tabloid reviews a show that he thinks fails in its ambitious aims.

The reader gets the same kind of information here. More than one tabloid must exist. The tabloid in question has one television critic. Identifying which tabloid is enough to establish which television critic.

I don't think the sentence about the television critic necessarily implies that the tabloid employs only one such critic. The 'the' refers to the critic who wrote the piece that the sentence refers to. That critic is one of something in the given context: the context comprises the writer of the piece we are talking about.

I am not really sure whether I can agree with your line of reasoning. It seems to me that by the same token you can replace all indefinite articles in the language with definite ones. Indeed, e.g. in my first sentence according to your logic the author should have written "the well-known television soap opera" because after all the author knows what opera is being discussed in the article of the tabloid.
– Sergey ZykovAug 9 '18 at 20:21

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@SergeyZykov Actually the author could indeed have written "the well-known television soap opera" because the subsequent reference to the "fictitious square" makes it quite clear what soap opera he is talking about. By the way, I am not using 'should' but 'could'. And it is not my reasoning, with which you are of course at liberty to disagree, but my observation of how the language is used by educated native speakers. If what such people write does not conform with what you have been told are rules, then so much the worse for the rules!
– JeremyCAug 9 '18 at 21:02